Initially there was the Microsoft Mobile Explorer (you can read more about it in What's special about the Microsoft Mobile Explorer?) which was a dual browser with WAP 1 and HTML capabilities. Later came PocketIE that featured a much better capability of rendering pages made for desktop computers on mobile devices.
IEMobile is the next incarnation of the mobile browser according to Microsoft. The browser was developed with PDA‘s and smartphones in mind, not the small devices that you fit in your pocket. The target user is an advanced user that will want to browse mobile sites, but also web sites that were originally aimed to desktop computers. It still supports markups made for the mobile (WAP 1 and 2), but also supports the modern HTML and XHTML markups.